# Comparative Analysis of the Efficiency of the

*Monte Carlo Technique and Intellectual Methods for the Reconstruction of Microstructural Parameters of Cloud Aerosol in the Scheme of Multi-Wavelength Lidar Sensing*

Earlier in Reference 22, we have carried out the comparative analysis of the efficiency of the inverse Monte Carlo method and intellectual methods for reconstruction of microstructural parameters of cloud aerosol in the scheme of multiwavelength lidar sensing. The analysis was performed within the framework of the closed computational experiment. The direct problem of estimation of backscattering signals within the scope of the nonstationary linear radiation transfer theory was calculated by the semianalytical Monte Carlo method allowing the boundary conditions of the real physical experiment to be taken into account quite rigorously. In this case, the physical prototype of the lidar was the mentioned mobile French-German Teramobile system, whose operational and technical characteristics are considered in detail in the literature [6]. The results of solution of the direct problem, that is, time scans of signals, obtained for the given set of wavelengths and satisfying the requirements of the informativeness, and the a priori known model of the cloudy atmosphere, were used for the reconstruction of optical and microphysical parameters of the atmosphere included in the model. The calculations were performed

282 ? *Optical Waves and Laser Beams in the Irregular Atmosphere *for four sensing wavelengths 1.28, 1.56, 1.61, and 2.13 pm, which fall within the near-IR micro-windows, according to our estimates. The middle-cyclic continental aerosol model was chosen as an optical model of the atmosphere [75]. A 100-m cloud layer was taken to be at a height of 200 m, and microphysics of the stratified- inhomogeneous cloud corresponded to commonly used test Cloud C1 model by Deirmendjan [69].

Examples of reconstruction of microphysical parameters of a cloud layer by different inversion methods are shown in Figures 5.14 through 5.16.

Figure 5.14 shows the vertical cross section of the cloud droplet size distribution function of the particle number density *N(r)* reconstructed with the use of the inverse Monte Carlo method. This method does not invoke a priori information about the form of the distribution function. Consequently, numerous solutions can be obtained, because they are not limited by one class of functions. To limit the number of possible solutions, the initial sample of radii is generated in a random way according to some probability density having the preset modal radius. Results obtained with the use of the Monte Carlo method show that this method begins to produce large deviations of large errors in backscattering coefficients. In addition, in real experiments, the modal radius is known only approximately, and, what is most important, to increase the accuracy of the method, it is needed to use the much greater number of sensing wavelength, which is instrumentally impossible now.

Then the genetic algorithm was used for solution of the problem, and the obtained results of reconstruction of the distribution function N(r) are shown in Figure 5.15. This algorithm has allowed an increase in accuracy of reconstruction of the distribution function. However, it should be noted that at the strong distortion

Figure 5.14 Vertical profile of the particle size distribution function of number density *N(r)* reconstructed by the inverse Monte Carlo method.

*Peculiarities of Propagation of Ultrashort Laser Pulses ?*

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Figure 5.15 Vertical profile of the particle size distribution function of number density *N(r)* reconstructed by the genetic algorithm.

of reconstructed profiles of the backscattering coefficient it is rather difficult to select the proper criterion for termination of the iteration process of the genetic algorithm, because the obtained solutions are limited to the class of gamma functions. In addition, a certain disadvantage of the genetic algorithm is its rather slow convergence, which complicates the use of this algorithm in real time. Nevertheless, the accuracy of reconstruction is rather high, because the model dependence of the backscattering coefficient on the wavelength is limited to some class of functions. This method can be successfully used for processing of actual data, because

Figure 5.16 Vertical profile of the particle size distribution function of number density *N(r)* reconstructed by the method neural network.

unimodal distribution functions N(r) in the most cases are well approximated by the generalized gamma distribution. In the case of complex composite distributions N(r), the larger number of sensing wavelengths should be invoked. However, numerical experiments have shown that, even with the use of many wavelengths in the limited class of functions N(r), several solutions of problem (5.45) can be obtained. In this case, it is unclear which solution corresponds to the actual one. It is often proposed [34,64] to obtain the averaged solution or to refine the solution with the aid of available a priori ideas about the distribution function.

Figure 5.16 shows vertical profiles of the distribution function N(r) for the analogous experimental model as reconstructed with the aid of the method of artificial neural networks. It can be said that the method of neural networks appeared to be somewhat more sensitive to errors of input values of backscattering coefficient profiles in comparison with the genetic algorithm, which is caused, to a large extent, by the retraining of NN with particular examples, as well as by the strong distortion of the backscattering coefficient. In addition, capabilities of the neural network are limited to the domain of learning examples. Therefore, if real or test values are outside the learning sample, then the network can yield inadequate or unreal solutions. However, this problem can be solved to a large extent through creation of the most complete learning sample. The neural network can solve the problem of reconstruction in real time, as well as it automatically solves the problem of multiple solutions of problem (5.45) by averaging them. Alternatively, this problem is solved at the stage of construction of the neural network and creation of the learning sample through introduction of the additional input of the neural network for a priori information (e.g., specification of the approximate value of the modal radius or the distribution half-width). A common disadvantage of the intellectual methods employing vertical profiles of backscattering coefficients *(**3*_{n}(*,* h), *i* = 1, ... , 4 reconstructed with the increasing error as input information, as follows from the analysis of Figures 5.15 and 5.16, remains the domain of stable solutions insufficient in the cloud depth.